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250119 VO Model theory (2021W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik
MIXED

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

Language: English

Lecturers

Classes (iCal) - next class is marked with N

Wednesday 06.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Friday 08.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Wednesday 13.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Friday 15.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Wednesday 20.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Friday 22.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Wednesday 27.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Friday 29.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Wednesday 03.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Friday 05.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Wednesday 10.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Friday 12.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Wednesday 17.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Friday 19.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Wednesday 24.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Friday 26.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Wednesday 01.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Friday 03.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Friday 10.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Wednesday 15.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Friday 17.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Friday 07.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Wednesday 12.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Friday 14.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Wednesday 19.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Friday 21.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Wednesday 26.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
Friday 28.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01

Information

Aims, contents and method of the course

Model theory is a branch of mathematical logic which applies the methods of logic to the study of mathematical structures, and thus has impact on other parts of mathematics (e.g., number theory, analytic geometry).

Since its beginnings in the early decades of the last century, the perception of what the subject is about has gone through various incarnations. A modern view holds that model theory is the "geography of tame mathematics" (Hrushovski), with the goal of identifying those classes of structures whose first-order theories can be understood (in some well-defined technical sense), and exploiting such an understanding as a tool in other parts of mathematics.

This course will serve as a first introduction to this multi-faceted subject. Both the development of general theory and some applications (mainly to algebra) will be presented.

Assessment and permitted materials

Grades will be based on homework sets assigned over the course of the semester.

Minimum requirements and assessment criteria

Examination topics

Review of structures, theories, ultraproducts, proof of the Compactness Theorem. Quantifier elimination, model completeness. Types, saturation, omitting types. Totally transcendental theories, strong minimality, Morley's Theorem. Other topics as time permits.

Reading list

I will follow my own notes, but some useful references for this class are:

C. C. Chang and H. J. Keisler, Model Theory, 3rd ed., Studies in Logic and the Foundations of Mathematics, vol. 73. North-Holland Publishing Co., Amsterdam, 1990.

W. Hodges, Model Theory, Encyclopedia of Mathematics and its Applications, vol. 42. Cambridge University Press, Cambridge, 1993.

D. Marker, Model Theory. An Introduction, Graduate Texts in Mathematics, vol. 217. Springer-Verlag, New York, 2002.

K. Tent, M. Ziegler, A Course in Model Theory, Lecture Notes in Logic, vol. 40, Cambridge University Press, Cambridge, 2012.

Association in the course directory

MLOV

Last modified: Th 23.09.2021 17:31